n one year the economy will either be weak, normal or strong. The respective probabilities of these three outcomes are $0\mathrm{.}37$ for weak, $0\mathrm{.}47$ for normal, and for strong you must determine it$.$ Three primitive securities exist that will each pay out $$100$ in one year depending on the state of the economy. The primitive that pays out in the weak economy has pricetoday of $$40\mathrm{.}91.$ The primitive that pays out in the normal economy has price today of $$39\mathrm{.}93.$ The primitive that pays out in the strong economy has price today of $$10\mathrm{.}73.$

Determine the risk$-$free rate of interest and enter it into the space provided.

Answer in $\%$ to four decimal places, do not include $\text{'}\%\text{'}$ in your answer $($e$.$g$.,12\mathrm{.}1234).$

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